OPTO-ELECTRONICS REVIEW 16(1), 34–41
DOI: 10.2478/s11772-007-0027-3
Solid State Crystals
Analysis of anticipated performance of 650-nm GaInP/AlGaInP
quantum-well GaAs-based VCSELs at elevated temperatures
£. PISKORSKI, R.P. SARZA£A, and W. NAKWASKI*
Institute of Physics, Technical University of £ódŸ, 219 Wólczañska Str., 93-005 £ódŸ, Poland
The possibility of application of the 650-nm oxide-confined GaInP/AlGaInP quantum-well vertical-cavity surface-emitting
diode lasers (VCSELs) at elevated temperatures as sources of the carrier 650-nm wave in the fibre optical communication using POFs has been investigated with the aid of the comprehensive self-consistent model. An increase in the VCSEL threshold
current at higher temperatures has been found to be mostly associated with both the carrier leakage from the valley of the
Ga0.43In0.57P quantum-well material to the X-valley of the (Al0.67Ga0.33)0.52In0.48P barriers and the band-to-band absorption
within the Ga0.52In0.48P layer of the band-gap comparable with the energy of emitted radiation. Nevertheless, the AlGaInP
VCSELs exhibit encouraging thermal behaviour with the characteristic temperature T0 equal to as much as 134 K for the active-region temperatures up to 357 K. For the 5-µm devices, the maximal achievable output has been determined to decrease
from a quite high value of 1.0 mW for 293 K to 0.6 mW for 320 K and to still high 0.33 mW for 340 K. However, an efficient
operation of the above VCSEL at elevated temperatures requires still some structure modifications leading to a reduction of
both the above effects, the electron leakage from the valley and the band-to-band absorption within GaInP layers.
Keywords: 650-nm VCSELs, GaInP/AlGaInP VCSELs, VCSEL operation at elevated temperatures.
1. Introduction
Short-wavelength lasing emission, especially that of 650
nm, may be applied in many various devices. Because of
its wavelength, much shorter than the wavelength of 850
nm of radiation emitted by standard arsenide diode lasers
used in compact disk (CD) devices, they ensure much
higher density of information in recording systems on digital versatile disks (DVDs). Analogously, the 650-nm radiation is widely used in laser printers. This radiation is also
used in many branches of medicine, e.g., in photodynamic
therapy. But its the most important application is associated
with communication networks taking advantage of plastic
(polymer) optical fibres (POFs) [1,2], for which the minimal optical attenuation corresponds to the 650-nm wavelength [3]. Because of relatively high POF mechanical flexibility and additionally their much larger core, for relatively
short distances and moderate data rates, POFs are currently
the lowest cost media to use for optical interconnect and
the simplest to connectorize [4–7]. There are still, however,
some technological and designing problems to produce
proper high-performance sources of the carrier wave used
in this communication networks.
Vertical-cavity surface-emission diode lasers (VCSELs)
compose the most suited laser configuration for the fibre
application. The desired 650-nm radiation may be emitted
*e-mail:
34
[email protected]
by the GaInP/AlGaInP quantum wells (QWs). Hence, the
GaAs-based oxide-confined (OC) VCSELs with the above
QWs [8] seem currently to be the best designs for the
POF-based fibre optical communication. This kind of communication is especially suited for cars, planes, and ships.
Therefore it should be resistant to some possible temperature increases. Accordingly, the main goal of this work is
to examine anticipated thermal properties of the 650-nm
AlGaInP VCSELs with the aid of a modified version of our
comprehensive self-consistent model [9] simulating a
VCSEL operation.
2. The model
Modelling of a high-temperature VCSEL performance requires application of a comprehensive approach. Therefore,
to simulate the continuous-wave (CW) operation of GaInP/
AlGaInP VCSELs at the temperatures higher than the room
temperature (RT), we have adapted, for higher temperatures and for the over-threshold operation, our three-dimensional optical-electrical-thermal-recombination self-consistent VCSEL threshold model reported earlier by Sarza³a
and Nakwaski [9]. The model consists of four mutually interrelated parts:
• optical model describing, for successive cavity modes,
their CW lasing thresholds, wavelengths, intensity profiles within the laser cavity, and absorption,
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• electrical model characterizing both the current spreading (including carrier diffusion) between the top and the
bottom contacts, the injection of carriers of both kinds
into the active region, their radial out-diffusion before
their recombination and the possible over-barrier leakage from the active region,
• thermal model characterizing generation of a heat flux
(non-radiative recombination, reabsorption of spontaneous radiation as well as volume and barrier Joule heating) and its spreading within the device from heat
sources towards the heat sink and within the heat sink,
• recombination model describing recombination processes within the QW active region, i.e., furnishing information about the optical gain process being a result
of the radiative bi-molecular recombination as well as
about the both non-radiative mono-molecular and the
Auger recombinations.
The above well-conducted self-consistent approach allows us integration of various physical phenomena taking
place within a VCSEL device and crucial for its CW operation with the aid of the self-consistent approach (Fig. 1).
There are three important features of the GaInP/
AlGaInP VCSELs which makes their high-temperature
CW lasing operation more troublesome than in the case of
standard GaAs/AlGaAs ones [10], smaller confining poten-
tial (shallower QWs), which means that the over-barrier
carrier leakage will be greater, larger electron and heavyhole effective masses, which contributes to higher threshold currents, and too wide band-gaps of some structure layers, which may lead to a band-to-band absorption. Besides,
higher carrier effective masses reduce efficiency of their
injection into distant QWs, which limits their available
numbers. Standard AlAs/GaAs distributed Bragg reflector
mirrors (DBRs) cannot be used for the visible radiation because of extremely high absorption in the GaAs layers. Instead, the AlAs/AlxGa1–xAs DBRs must be used with a relatively high x mole fraction, which drastically reduces the
refractive index contrast ratio DnR/nR. For x = 0.5, DnR/nR =
11% and as many as 34 DBR periods are needed to reach
over 99.9% DBR reflectivity. Consequently, thicker DBRs
lead to the higher both the series electrical resistance and
the thermal resistance which is followed by the higher active-region temperatures. Besides, because of absorption,
radiation cannot be emitted through the GaAs substrate
which limits designing possibilities.
All the above features are introduced here into our previous comprehensive model [9] of the GaAs-based
GaInNAs VCSELs with the aid of appropriate model parameters (see below). But there is also one new feature
which has not been included in the previous model because
Fig. 1. The flow chart of the self-consistent optical-electrical-thermal-recombination VCSEL simulation.
Opto-Electron. Rev., 16, no. 1, 2008
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Analysis of anticipated performance of 650-nm GaInP/AlGaInP quantum-well GaAs-based VCSELs...
of its negligible impact on properties of the above VCSELs
and which has happened to be extremely important in the
GaInP/AlGaInP one. In the AlGaInP compounds, the
crossover of the direct and indirect band gaps occurs at 300
K for the (Al0.58Ga0.42)0.5In0.5P material [11], which limits
shorter-wavelength operation to about 555–570 nm and
band-gap energies available for barrier and cladding materials [10]. Even for somewhat longer wavelengths, the
higher active-region temperatures may lead to the considerable electron leakage (Fig. 2) from the G valley of the
Ga0.43In0.57P quantum-well material to the X-valley of the
(Al0.67Ga0.33)0.52In0.48P barriers [12] which are very close
on the energy scale. This phenomenon is especially important in the case of the 665-nm VCSELs [13] and even more
considerable in the 630-nm ones [14]. In our model, the
above effect has been additionally taken into account by introduction of the temperature-dependent efficiency inj of
electron injection into the active region
h inj = aT A,max + b
(1)
where TA,max stands for the maximal active-region temperature and values of the a = –175–1 K–1 and b = 2.6 parameters have been extracted from Fig. 2(a) in the paper of
Knowles et al. [12]. Besides, the strong gain-cavity alignment effect [15] is taken into consideration.
Electrical conductivities of semiconductor layers depend on their doping and temperature. With the aid of the
approach given in the Appendix of Ref. 16, their values
Fig. 2. Band structure of a surrounding of the Ga0.43In0.57P/
(Al0.50Ga0.50)0.52In0.48P multiple-quantum-well (MQW) active
region used in the VCSEL under consideration. z is a distance from
the n-GaAs substrate. Ev stands for the edge of the valence band,
whereas Ec,G and Ec,X are analogous edges of the conduction band
of the G and X valleys, respectively. e0 and e1 indicate first two
electron levels within the conduction-band QW, whereas hh0, hh1,
lh0 and lh1 show analogous first two levels of heavy holes and light
holes, respectively, within the valence band QW.
have been determined using the data reported in Refs.
16–26 and those of metallic layers in Refs. 27 and 28. For
two temperatures of 300 K and 400 K, electrical conductivities of successive semiconductor layers (together with
metal ones) are listed in Table 1. For the AlGaAs material,
Table 1. Electrical conductivities of materials used in the GaInP/AlGaInP VCSEL under consideration.
Doping concentration
(1024 m–3)
s (300 K)
(1/Wm)
s (400 K)
(1/Wm)
p-GaAs
40
50786
36404
p-Ga0.52In0.48P
2
1101
770
p-Al0.50Ga0.50As
3
2846
1997
p-Al0.95Ga0.05As
8
4489
3243
p-Al0.98Ga0.02As
8
4385
3177
p-(Al0.67Ga0.33)0.52In0.48P
0.5
56
49
n-(Al0.67Ga0.33)0.52In0.48P
1
1073
749
n-Al0.50Ga0.50As
2
2398
1943
n-AlAs
2
4253
2850
n-GaAs substrate
10
297760
207313
AlxOy
–
1×10–4
1×10–4
Ti
–
2.340×106
1.705×106
Pt
–
9.259×106
6.849×106
Au
–
4.403×107
3.218×107
Ni
–
1.389×107
0.848×107
In
–
1.160×107
1.160×107
Cu
–
5.797×107
4.163×107
Layer
36
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its thermal conductivity has been given by Adachi [29] and
its temperature dependence by Amith et al. [30]. Analogous values for the GaInP material and the AlGaInP material have been extracted from the papers published by
Adachi [29], Nakwaski [31], and Guden and Piprek [32].
Because of extremely thin QW layers, the whole active region has been assumed to exhibit the thermal conductivity
of the barriers. Temperature dependences of thermal conductivities of most of the metal layers have been found in
the book of Weber [27] with an exception of ind, for which
a constant RT value has been taken from http://www.matter-antimatter.com. Temperature-independent thermal conductivity of the AlxOy has been assumed to be equal to that
determined by Le Dõ et al. [33]. Values of thermal conductivities have been listed in Table 2. For the bottom heatsink surface, the surface conductance coefficient of 50
W/m2K has been assumed.
The flow chart of our fully self-consistent calculation
algorithm is shown in Fig. 1. The model considers all important interactions between individual physical phenomena taking place within the VCSEL volume, including:
• thermal focusing, i.e., the temperature dependence of
refractive indices,
• self-focusing, i.e., the carrier-concentration dependence
of refractive indices,
• gain-induced wave-guiding, i.e. the temperature, carrier-concentration and wavelength dependences of the
extinction coefficient,
• temperature dependence of thermal conductivities,
• temperature and carrier-concentration dependences of
electrical conductivities,
• temperature, carrier-concentration and wavelength dependences of optical gain and absorption coefficients,
• temperature and carrier-concentration dependences of
the energy gaps.
Accordingly, three-dimensional (3D) profiles of all
model parameters within the whole device volume are determined not only on the basis of various chemical compositions of its structure layers but also taking into account
current 3D profiles of the temperature, the current density,
the carrier concentration and the mode radiation intensity,
all of them with the aid of the self-consistent calculation algorithm shown in Fig. 1. The model has been developed
following VCSEL modelling rules reported by Osiñski and
Nakwaski [34].
3. The structure
The structure, very similar to the currently most modern
650-nm AGaInP/AlGaInP GaAs-based VCSEL, proposed
by Knigge et al. [8] has been chosen (Fig. 3) to determine
some of its anticipated performance characteristics. Its intentionally undoped active region is assumed to be composed of three 4.4-nm Ga0.43In0.57P QWs [multi-quantumwell (MQW) structure] separated by the 8.7-nm
(Al0.50Ga0.50)0.52In0.48P internal barriers. External 19.5-nm
Opto-Electron. Rev., 16, no. 1, 2008
Table 2. Thermal conductivities k of materials used in the
GaInP/AlGaInP VCSEL under consideration.
Layer
k (300 K)
(W/mK)
k (400 K)
(W/mK)
GaAs
44.05
30.75
Al0.50Ga0.50As
10.89
7.60
Al0.95Ga0.05As
38.71
27.02
Al0.98Ga0.02As
58.43
40.78
AlAs
90.91
63.45
Ga0.52In0.48P
15.75
14.07
Ga0.43In0.57P (QW)/
(Al0.50Ga0.50)0.52In0,48P (B)
7.50
7.13
(Al0.67Ga0.33)0.52In0.48P
6.36
6.11
AlxOy
0.7
0.7
Ti
21.9
20.4
Pt
71.6
71.8
Au
317
311
Ni
90.7
80.2
In
81.6
81.6
Cu
401
393
barriers (B) manufactured from the same material as the internal ones are assumed on both MQW sides. The active region is sandwiched by the 63.4-nm (Al0.67Ga0.33)0.52In0.48P
spacers, doped with silicon (1018 cm–3) or zinc (5×1017
cm–3) on the n and p sides, respectively. The ë cavity is terminated on both sides by distributed-Bragg-reflectors
(DBRs), the 35-pair Al0.5Ga0.5As (47.2 nm)/Al0.95Ga0.05As
(52.0 nm) p-side DBR and the 55.5-pair Al0.5Ga0.5As (47.2
nm)/AlAs (52.2 nm) n-side DBR. In both DBRs, the higher
Al-content layers are situated as the first ones from the cavity side. The third (counting from the cavity) Al0.95Ga0.05As
layer in the p-side DBR is replaced by the 52.3-nm
Al0.98Ga0.02As one to enable its efficient radial oxidation
necessary to create the appropriate AlxOy oxide aperture.
The bottom n-type DBR is doped with silicon up to 2×1018
cm–3, whereas the upper p-side one is doped with carbon
up to 8×1018 cm–3 (higher-AlAs content layers) and 3×1018
cm–3 (lower-AlAs content layers). The upper DBR is covered with the 10-nm Ga0.52In0.48P layer (doped with zinc up
to 2×1018 cm–3) to protect the high AlAs-content DBR layers from oxidation. Its composition was intentionally chosen to reduce a possible absorption of the laser radiation.
However, this absorption becomes considerable in the case
of temperatures exceeding 350 K, for which the layer energy gap is eventually equal to the energy of the 650-nm
radiation. DBR diameters are assumed to be equal to 35 µm
(upper DBR) and 60 µm (bottom DBR). The upper p-side
contact is produced in a form of a ring of the 19-µm internal diameter. It is separated from the Ga0.52In0.48P layer
with the highly doped with zinc (4×1019 cm–3) ring GaAs
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Analysis of anticipated performance of 650-nm GaInP/AlGaInP quantum-well GaAs-based VCSELs...
Fig. 3. Modelled structure of the oxide-confined GaInP/AlGaInP QW VCSEL emitting radiation of the wavelength of 650 nm.
layer. The whole bottom 60-µm diameter surface of the
150-µm GaAs substrate doped with silicon up to 1019 cm–3
is covered by the n-side contact. The laser is attached to the
cylindrical (height = diameter = 5 mm) copper heat sink
with the 5-µm indium solder. Compositions and doping
values of all structure layers are listed in Table 1.
4. Results
The model presented in Sec. 2 is used to determine some
performance characteristics of the laser under consideration. An increase in the ambient temperature Tamb is followed by important changes of values of material parameters, for example values of carrier mobilities, energy gaps,
efficiency of radiative recombination and thermal conductivities are reduced, whereas those of coefficients of optical
absorption, efficiencies of non-radiative recombinations
and refractive indices are increased, to name the most important changes. As a result, all important physical phenomena taking place within a VCSEL volume during its
operation, i.e., current spreading, carrier diffusion and their
later recombination, carrier leakage from the QW active region, confinement of an optical field, radiation absorption,
heat-flux generation and extraction etc., are considerable
changed and hence a VCSEL performance is essentially
deteriorated, its threshold current is increased and its quantum efficiency is reduced. For too high ambient temperatures, a VCSEL lasing becomes impossible. It is interesting
to note that the maximal active-region temperature TA,max is
for a lasing threshold of the VCSEL under consideration
directly proportional to Tamb, dTA,max/dTamb = 1.1.
An increase in the ambient temperature Tamb causes an
increase in the threshold bias voltage Uth of the 5-µm oxide-confined GaInP/AlGaInP QW VCSEL shown in Fig. 4.
Its form resembles an exponential curve. At higher temperatures, higher bias voltage is necessary because higher operation current is needed to reach increasing lasing threshold. Radial profiles of the threshold current densities jth are
plotted for successive ambient temperatures in Fig. 5. As
one can see, current injection into the active region remains
38
quite uniform but, similarly as in the case of Uth, threshold
current densities increase super-linearly with Tamb, which is
a direct consequence of increasing problems with reaching
the lasing threshold at higher temperatures. Carriers injected into the active region diffuse in the radial direction
until their recombination, radiative bimolecular or nonradiative monomolecular and Auger ones. Radial profiles
of the threshold carrier concentrations nth at the moment of
their recombination are shown in Fig. 6. Analogous profiles of the optical threshold gain have very similar forms.
Their bell-like distributions are profitable for an excitation
of the fundamental LP01 mode because of their high overlapping with its centrally located radial intensity distribution. Threshold carrier concentration increase with the ambient temperature Tamb is surprisingly less pronounced than
that of the threshold current density because of an increasing importance of the current leakage shown below.
A relative share of the carrier leakage and all three recombination processes within the total threshold current is
shown as a function of the ambient temperature in Fig. 7.
The radiative bi-molecular recombination has been found
Fig. 4. An increase in the threshold bias voltage Uth of the 5-µm
oxide-confined GaInP/AlGaInP QW VCSEL as a function of the
ambient temperature Tamb.
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Fig. 5. Radial profiles of the threshold current density jth of the
5-µm oxide-confined GaInP/AlGaInP QW VCSEL plotted for
various ambient temperatures Tamb.
Fig. 6. Radial profiles of the threshold carrier concentration nth of
the 5-µm oxide-confined GaInP/AlGaInP QW VCSEL plotted for
various ambient temperatures Tamb.
to be a dominating process at RT, but, at higher temperatures, an impact of the leakage current becomes much more
important. Nevertheless, the characteristic temperature
(T0 = 134 K) remains quite high within the active-region
temperatures not exceeding 357 K.
Gain spectra of the Ga0.43In0.57P/(Al0.50Ga0.50)0.52In0.48P
QW used in the VCSEL under consideration determined
for the constant carrier concentration of 6×1018 cm–3 and
for various active-region temperatures TA are shown in
Fig. 8. As one can see, with an increase in TA, a shift of the
gain spectrum towards longer wavelengths together with a
gradual reduction of its maximal achievable value is observed. The optical gain g650 for the radiation of the wavelength 650 nm determined for various active-region temperatures as a function of the carrier concentration n is plotted in Fig. 9. The carrier concentration ntr, corresponding to
Opto-Electron. Rev., 16, no. 1, 2008
Fig. 7. Relative share of individual recombination processes, the
radiative bi-molecular recombination (Irad) and the both non-radiative mono-molecular (ISRH) and Auger (IAuger) recombinations, as
well as the carrier leakage (Ileak), in the total threshold current
(Itotal) of the 5-µm oxide-confined GaInP/AlGaInP QW VCSEL as
a function of the ambient temperature Tamb.
Fig. 8. Gain spectra of the Ga0.43In0.57P/(Al0.50Ga0.50)0.52In0.48P
QW at various active-region temperatures TA for the constant
carrier concentration of 6×1018 cm–3.
the g650 = 0 value, is called the transparency concentration.
It is interesting to note that a saturation of the gain behaviour is more considerable at lower temperatures.
The emission characteristics, i.e., the output power P as
a function of the operation current I of the 5-µm oxideconfined GaInP/AlGaInP QW VCSEL are plotted for various ambient temperatures Tamb in Fig. 10. The threshold
current is practically identical for both the lowest temperatures which follow from opposite influences of a profitable
shift with a temperature of the gain spectrum towards longer wavelengths and a simultaneous reduction in the maximal achievable gain (Fig. 9). A considerably higher threshold determined for Tamb = 340 K is a result of an increasing
band-to-band absorption within the thin upper contact
Ga0.52In0.48P layer because at 335 K its band-gap becomes
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Analysis of anticipated performance of 650-nm GaInP/AlGaInP quantum-well GaAs-based VCSELs...
within GaInP layers of band-gaps comparable with the energy of emitted radiation.
Acknowledgements
The authors would like to acknowledge support from the
Polish Ministry of Science and Higher Education
(MNiSzW), grant No 3-T11B-073-29.
References
Fig. 9. Optical gain g650 for the radiation of the 650-nm wavelength
of the Ga0.43In0.57P/(Al0.50Ga0.50)0.52In0.48P QW at various activeregion temperatures TA as a function of the carrier concentration n.
Fig. 10. The emission characteristics, i.e., the output power P as a
function of the operation current I, of the 5-µm oxide-confined
GaInP/AlGaInP QW VCSEL plotted for various ambient
temperatures Tamb.
equal to the energy of the 650-nm radiation. As one can
see, the maximal achievable VCSEL output is quite high
and is decreased from 1.0 mW for 293 K to 0.6 mW for
320 K and to 0.33 mW for 340 K.
5. Conclusions
The oxide-confined GaInP/AlGaInP quantum-well vertical-cavity surface-emitting diode lasers (VCSELs) have
been found to be at a room temperature (RT) very promising laser sources of the 650-nm carrier wave for the optical
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40
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